The electric current in the circuit is given as i = i 0 ( t T ) . The r.m.s current for the period t = 0 to t = T is_______. [2026]

Question

The electric current in the circuit is given as $i = i_{0} ((\frac{t}{T})) .$ The r.m.s current for the period $t = 0 to t = T$ is_______. [2026]

Smart Achievers · Accepted Answer

(1)

$i_{rms}^{2} = \frac{\int_{0}^{T} (\frac{i_{0}^{2} t^{2}}{T^{2}}) d t}{\int_{0}^{T} d t} = \frac{i_{0}^{2}}{T^{3}} \cdot \frac{T^{3}}{3} = \frac{i_{0}^{2}}{3}$

$i_{rms} = \frac{i_{0}}{\sqrt{3}}$

Solution

Q.
The electric current in the circuit is given as $i = i_{0} ((\frac{t}{T})) .$ The r.m.s current for the period $t = 0 to t = T$ is_______. [2026]

1 $\frac{i_{0}}{\sqrt{3}}$

2 $\frac{i_{0}}{\sqrt{2}}$

3 $\frac{i_{0}}{\sqrt{6}}$

4 $i_{0}$

Ans.
(1)

$i_{rms}^{2} = \frac{\int_{0}^{T} (\frac{i_{0}^{2} t^{2}}{T^{2}}) d t}{\int_{0}^{T} d t} = \frac{i_{0}^{2}}{T^{3}} \cdot \frac{T^{3}}{3} = \frac{i_{0}^{2}}{3}$

$i_{rms} = \frac{i_{0}}{\sqrt{3}}$

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Solution

Q. The electric current in the circuit is given as i=i0(tT). The r.m.s current for the period t=0 to t=T is_______. [2026]

1 i03

2 i02

3 i06

4 i0

Ans. (1) irms2=∫0T(i02t2T2)dt∫0Tdt=i02T3·T33=i023 irms=i03